(ns com.yawmark.euler.clj.e11)

; In the 20X20 grid below, four numbers along a diagonal line have been
; marked in red.
; 
; 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
; 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
; 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
; 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
; 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
; 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
; 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
; 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
; 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
; 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
; 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
; 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
; 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
; 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
; 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
; 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
`; 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
; 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
; 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
; 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
;
; The product of these numbers is 26  63  78  14 = 1788696.
; 
; What is the greatest product of four adjacent numbers in any
; direction (up, down, left, right, or diagonally) in the
; 20X20 grid?

(def grid [
            8  2 22 97 38 15  0 40  0 75  4  5  7 78 52 12 50 77 91  8 
           49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48  4 56 62  0 
           81 49 31 73 55 79 14 29 93 71 40 67 53 88 30  3 49 13 36 65 
           52 70 95 23  4 60 11 42 69 24 68 56  1 32 56 71 37  2 36 91 
           22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 
           24 47 32 60 99  3 45  2 44 75 33 53 78 36 84 20 35 17 12 50 
           32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 
           67 26 20 68  2 62 12 20 95 63 94 39 63  8 40 91 66 49 94 21 
           24 55 58  5 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 
           21 36 23  9 75  0 76 44 20 45 35 14  0 61 33 97 34 31 33 95 
           78 17 53 28 22 75 31 67 15 94  3 80  4 62 16 14  9 53 56 92 
           16 39  5 42 96 35 31 47 55 58 88 24  0 17 54 24 36 29 85 57 
           86 56  0 48 35 71 89  7  5 44 44 37 44 60 21 58 51 54 17 58 
           19 80 81 68  5 94 47 69 28 73 92 13 86 52 17 77  4 89 55 40 
            4 52  8 83 97 35 99 16  7 97 57 32 16 26 26 79 33 27 98 66 
           88 36 68 87 57 62 20 72  3 46 33 67 46 55 12 32 63 93 53 69 
            4 42 16 73 38 25 39 11 24 94 72 18  8 46 29 32 40 62 76 36 
           20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74  4 36 16 
           20 73 35 29 78 31 90  1 74 31 49 71 48 86 81 16 23 57  5 54 
            1 70 54 71 83 51 54 69 16 92 33 48 61 43 52  1 89 19 67 48 ])

(def indexes (range (* 20 20)))

(defn get-groups [group-def]
  (map #(take 4 (take-nth (group-def :offset) (subvec grid %)))
       (filter (group-def :filter) indexes)))

(defn right-filter [idx] (< (mod idx 20) 17))
(defn left-filter [idx] (> (mod idx 20) 2))
(defn down-filter [idx] idx)

(defn groups []
     (concat (get-groups {:offset 1    :filter right-filter })
             (get-groups {:offset 20   :filter down-filter  })
             (get-groups {:offset 19   :filter left-filter  })
             (get-groups {:offset 21   :filter right-filter })))

(defn euler-11 []
  (apply max (map #(reduce * %) (groups))))

(time (println (euler-11)))

(def matrix [
             [  8  2 22 97 38 15  0 40  0 75  4  5  7 78 52 12 50 77 91  8 ]
             [ 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48  4 56 62  0 ]
             [ 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30  3 49 13 36 65 ]
             [ 52 70 95 23  4 60 11 42 69 24 68 56  1 32 56 71 37  2 36 91 ]
             [ 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 ]
             [ 24 47 32 60 99  3 45  2 44 75 33 53 78 36 84 20 35 17 12 50 ]
             [ 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 ]
             [ 67 26 20 68  2 62 12 20 95 63 94 39 63  8 40 91 66 49 94 21 ]
             [ 24 55 58  5 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 ]
             [ 21 36 23  9 75  0 76 44 20 45 35 14  0 61 33 97 34 31 33 95 ]
             [ 78 17 53 28 22 75 31 67 15 94  3 80  4 62 16 14  9 53 56 92 ]
             [ 16 39  5 42 96 35 31 47 55 58 88 24  0 17 54 24 36 29 85 57 ]
             [ 86 56  0 48 35 71 89  7  5 44 44 37 44 60 21 58 51 54 17 58 ]
             [ 19 80 81 68  5 94 47 69 28 73 92 13 86 52 17 77  4 89 55 40 ]
             [  4 52  8 83 97 35 99 16  7 97 57 32 16 26 26 79 33 27 98 66 ]
             [ 88 36 68 87 57 62 20 72  3 46 33 67 46 55 12 32 63 93 53 69 ]
             [  4 42 16 73 38 25 39 11 24 94 72 18  8 46 29 32 40 62 76 36 ]
             [ 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74  4 36 16 ]
             [ 20 73 35 29 78 31 90  1 74 31 49 71 48 86 81 16 23 57  5 54 ] ])

(defn go-right [from-point]
  (take 4 (iterate (fn [[x y]] [x (inc y)]) from-point)))
(defn go-down [from-point]
  (take 4 (iterate (fn [[x y]] [(inc x) y]) from-point)))
(defn go-down-right [from-point]
  (take 4 (iterate (fn [[x y]] [(inc x) (inc y)]) from-point)))
(defn go-down-left [from-point]
  (take 4 (iterate (fn [[x y]] [(inc x) (dec y)]) from-point)))

(defn get-group [point dir]
  (filter #(not (nil? %)) (map #(get-in matrix %) (dir point))))

(defn get-groups [point dirs]
  (map #(get-group point %) dirs))

(defn sum-group [group] (reduce * group))
(defn sum-groups [groups]
  (map sum-group groups))
(defn points [] (for [x (range 20) y (range 20)] [x y]))

